### Abstract

Let G be a graph in which each edge is contained in at least one triangle (complete subgraph on three vertices). We investigate relationships between the smallest cardinality of an edge set containing at least i edges of each triangle and the largest cardinality of an edge set containing at most j edges of each triangle (i, j ∈ {1, 2}), and also compare those invariants with the numbers of vertices and edges in G. Several open problems are raised in the concluding section.

Original language | English |
---|---|

Pages (from-to) | 89-101 |

Number of pages | 13 |

Journal | Discrete Mathematics |

Volume | 150 |

Issue number | 1-3 |

Publication status | Published - Apr 6 1996 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*150*(1-3), 89-101.

**Covering and independence in triangle structures.** / Erdős, P.; Gallai, Tibor; Tuza, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 150, no. 1-3, pp. 89-101.

}

TY - JOUR

T1 - Covering and independence in triangle structures

AU - Erdős, P.

AU - Gallai, Tibor

AU - Tuza, Z.

PY - 1996/4/6

Y1 - 1996/4/6

N2 - Let G be a graph in which each edge is contained in at least one triangle (complete subgraph on three vertices). We investigate relationships between the smallest cardinality of an edge set containing at least i edges of each triangle and the largest cardinality of an edge set containing at most j edges of each triangle (i, j ∈ {1, 2}), and also compare those invariants with the numbers of vertices and edges in G. Several open problems are raised in the concluding section.

AB - Let G be a graph in which each edge is contained in at least one triangle (complete subgraph on three vertices). We investigate relationships between the smallest cardinality of an edge set containing at least i edges of each triangle and the largest cardinality of an edge set containing at most j edges of each triangle (i, j ∈ {1, 2}), and also compare those invariants with the numbers of vertices and edges in G. Several open problems are raised in the concluding section.

UR - http://www.scopus.com/inward/record.url?scp=0042632393&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042632393&partnerID=8YFLogxK

M3 - Article

VL - 150

SP - 89

EP - 101

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -